# Why are There Two Tides?

Date: 1995/07/02
organization: Seanet Online Services, Seattle WA
newsgroups: sci.physics
MessageID: 3t55mb\$oe9@kaleka.seanet.com
Subject: Why are there two tides?

Perhaps if everyone used the same terminology it would help. There are 3 different angular motions:

• 1. The daily rotation (spin) of the earth about the north/south axis;
• 2. The (Lunar) monthly revolution of the earth's center about the barycenter (center of mass of the earth/moon system);
• 3. The annual revolution of the barycenter about the sun.

Those claiming errors in my original explanation for the high tides question:

1. The frame of reference;
2. The direction of the gravity of the moon at the far side from the moon;
3. My contention that the earth/moon pair rotates about the barycenter;
4. And most of all, the use of centrifugal force in my explanation.

The tides are in angular acceleration as these follow the moon, as is the moon in acceleration, but at a different rate in its elliptical orbit. These and the geological features of the earth upon which the tides are measured, because of the daily rotation and orbit of the earth, are all in different non- inertial frames of reference. With the exception of one responder, all the critics of my original post have placed all in the same inertial frame of reference, and looked upon the tides, earth, and moon as in the same state of constant velocity.

SR basically states; 1, one cannot tell which body is moving and which is not moving when all are in the same inertial frame of motion, and that GR must be employed in non-inertial frames of reference; and 2, c is a constant. GR basically states that: 1, one cannot differentiate between gravitational and acceleration forces; and 2, mass tells space-time how to curve, and the curvature of space-time (gravity, inertia, and acceleration are all associated with the way space and time are related) tells mass how to accelerate. GR does not change the basic properties of gravity from that of Newtonian mechanics. Gravity still originates from mass, and the gravitational field of a mass is towards the mass.

In the frame of reference of the seashore where the tides are measured, the seas are moving up and down very slowly, and is measured in feet. The crest of the high tides (which are curved north/south lines that are impossible to accurately define, not a point, and oceanographers have identified about 54 factors that can modify it) are coming from the eastern horizon and traveling to the western horizon at little over 1000 mph along the curvature of the earth. And there are usually two high tides daily, usually of different heights. The sun and moon rise in the east and set in the west once a day, but their relationship to one another is constantly changing.

In the frame of reference of the crest of the high tides (and there are two, each different, due to different forces), the earth is moving up and down inconsistently once a day, and varies day to day. The geological features are moving from the WEST to the EAST at about 1000 mph, on the surface of the earth. The moon cycles slowly closer and farther once a lunar month, but stays in the same general spot in the sky. Of course the high tide at the far side from the moon can't see the moon. From the perspective of the crest(s), the sun seems to do its own thing in the sky, rising in the east and setting in the west once each lunar month. The sun's cycle is opposite for the two high tides, being 1/2 lunar month apart. The sun is rising for one when it sets for the other.

In the frame of reference of the moon, well you can see that it's different from that of the tides, earth or sun. And all are moving in angular acceleration still differently in the frame of reference of the sun. Just as an observer on the ground can't feel what the jet pilot feels, the tide measurers at the seashore can't exactly describe the forces on the tides to explain why these act the way these do, using only the forces within their frame of reference.

But the main point is; no one uses GR to explain the orbit of the moon about the earth, or even the orbit of the earth/moon pair about the sun. Good old classical Newtonian mechanics is employed, as any error introduced disregarding the curvature of space-time is negligible at this level. The precession of the planet Mercury's orbit is off only about 43 seconds of arc per century when using Newtonian mechanics. So classical mechanics can explain the tides.

A common mistake is confusing motion and force. When only forces are isolated, and any motion due to the force is put off until later, the gravitational field of the earth is towards the earth. The gravitational field of the moon is towards the moon. When the two are viewed as a pair, the gravitational forces of the moon are still towards the moon, whether at the side of the earth towards the moon or at the side away from the moon. The vector of the gravitational field of the moon does not change 180 degrees just because a mass intervenes. Even in GR, the gravity of the moon is towards the moon. GR does not explain 180 degree turns of gravitational fields, (with the unlikely possibility of those internal to a black hole.) Definitely not when a small mass (like that of the earth) is involved. Even the mass of stars deviate the direction of light only a few seconds of arc. So the gravities of the earth and moon are additive at the far side from the moon.

Now consider any motion due to the greater forces at the far side from the moon, and the seas move closer to the earth, and results in a low tide. Another force is required to raise the tides above this level at the far side. Acceleration forces. And so what if the tides can't differentiate the accelerative forces from gravity, it still rises above the mean sea level due to the acceleration forces. And so what if today's predictions of the tides 25 years hence are off a couple of inches and a few minutes. No one publishes 25 year tide tables, or to this precision, so no one could spot the errors if these were.

Another point about motion. Astronomers have known of binary stars for a long time, and understand the mechanics of these motions. The binary stars AND the earth/moon pair rotates about their common center of mass, the barycenter. It appears some can't view the earth and moon as an ordinary binary system, and don't apply these same principles to the earth/moon system. Apparently they see the earth as unique. They just can't seem to shake off the earth centered universe idea.

I know that 'centrifugal force' is a colloquialism, and is scientifically incorrect. (As do the aerospace scientists, but they're not afraid of the word, and don't get all shook up when it's used. I hope the critics realize 'black hole' is also a colloquialism. I hope they don't think it is a void in space, absent of mass. Off hand, I can't remember the exact definition of black hole right now, but it's awkward to keep repeating.) It seems many accept 'centrifugal force' is wrong, but don't know why. Then, because the term is scientifically incorrect, believe WHAT it represents does not exist. The forces represented by 'centrifugal force' are real! This term is commonly used to describe the force that 'throws' the stone from the sling of David and Goliath fame, and the force a fighter pilot feels during high speed turns.

This is due to several misunderstandings. Newton's third law of motion is often assumed to be the determining principle, but it is Newton's first law in the case of the sling. The inertia of the stone tends to keep the stone moving in a straight line at a given velocity. The pouch of the sling restrains the stone to follow the arc of the swing. The radius of the arc is fixed by the sling. The pouch applies a centripetal force on the stone to change its motion from the straight path described by Newton's first law. The tangential momentum described by Newton's first law is not fixed, and varies with the radius and speed of the swing. As soon as the centripetal force of the pouch is removed, the stone flies straight, tangent to the arc of the swing due to inertia.

The high tides follow the same principle, but are slightly different.

If centripetal force is the only force causing the tides, and if the gravity of the earth is the centripetal force, then gravity, being for all practical purposes fixed at the surface of the earth, being fixed by the radius of the earth, is a constant. Then the seas would remain fixed at the mean sea level, without high or low tides. If the much lesser gravity of the moon (all pull, no push) is entered into this condition, the forces are increased above those of only that of the earth's gravity at the far side from the moon, and when motion is introduced, there would be a low tide at this location because of the greater force.

Unlike the sling, the change of the motion from that described by Newton's first law is not fixed with the tides. The inertia of the seas, due to its fixed surface speed (not angular rate) of rotation, but changing radius of rotation, (measured from the changing barycenter to the crest of the tide), is not a constant. The constant gravity of the earth and very slightly changing, but lesser, gravity of the moon (the sum of which is the centripetal force at the far side from the moon) counters this changing inertia of the seas at this side of the earth. The very slightly greater (about 6%, debate this figure if you must, I won't argue that it's correct) gravity of the moon at the near side is in tandem with the inertia (about 1/7th of that at the far side) at the side facing the moon, and the much greater gravity of the earth (the same on both sides, and is the centripetal force on this side) counters both. The sun adds its bit.

So it is the summation of all the gravitational forces (the moon's is not a constant) acting differently on the changing inertia of the seas that cause the high tides. The high tides cannot be explained by centripetal force(s) or gravity(ies), alone.

A cause of the confusion about 'centrifugal force' is the belief that Newton's third law is only: "To every action there is an equal and opposite reaction". Not realizing that this is not the complete law as conceived by Newton has caused many to confuse motion with force, and miss the point that the reaction force is applied on the body applying the action force. But because of the misunderstanding of the third law, it is commonly believed that the reaction (mentioned in the third law) pertains to the motions of the mass upon that which the centripetal force is applied. As the straight line motion of the stone from the sling is due to inertia, and the motion of the pilot is due to the centripetal force of the plane, 'centrifugal force' per se, does not exist in this line of thinking.

To make everything short, Newton wrote in Latin, and the prevailing version is a mis-restatement of a translation. A true restatement of the third law of motion as conceived by Newton is: "As the action force of a body is the motive force applied by this body, and for every action force of a body there is an equal and opposite reaction force placed upon this same body; and as the total forces of two interacting bodies is the sum of their action forces; so the total motive force acting upon each of two interacting bodies is the summation of the reaction to the action force of one and the action force of the other, and these total forces are always equal and oppositely directed on each other." (There is absolutely no mention of motion in Newton's third law, only forces. Any motion due to the forces explained by the third law are described by the first two laws of motion.) This unwieldy restatement can be condensed to:

### LAW III

To every action there is an equal and opposite reaction;
so the total motive force acting upon each of two interacting bodies is the sum of their actions,
and is always equally and oppositely directed on each other.

In the example of the centrifuge, the contents is an inactive mass, and does not apply an action on the centrifuge. The action of the centrifuge applies an action force on the contents, and the reaction to this force is on the centrifuge. In Newtonian mechanics, the reaction force (the centrifugal force) on the centrifuge is equal and opposite to the action force (the centripetal force) on contents, so the total forces on both are equal and opposite, as explained by the true interpretation of Newton's third law.

Those denying the existence of the forces represented by 'centrifugal force' must also repudiate Newton's third law of motion in the cases of the centrifuge and jet pilot, or inertia in the case of the stone from the sling.

This restatement of the third law may not be a big deal to engineers, but should be to scientists. This explains the true connection between Newton's third law of motion and the principle of the conservation of momentum, and why the principle of the conservation of momentum agrees with the third law when bodies of unequal momentum interact and the bodies apply unequal actions upon each other. One must be ever mindful of differentiating between the total forces ON a body from those applied BY this body. While the magnitude may be equal in some cases, these are different things. When bodies of unequal momentum interact, even the magnitudes differ. The bit about Newton's third law is a very condensed version of that in the same copyrighted work as the tides, titled: "Handgun Recoil, Some Other Stuff and Isaac Newton, or the fundamentals of motion." This last statement is for legal purposes, 'on advice of attorney', it is not to push the writing.